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All Journal Jurnal Kimia (Journal of Chemistry) Jurnal Matematika Buletin Udayana Mengabdi E-Jurnal Matematika Bumi Lestari BAREKENG: Jurnal Ilmu Matematika dan Terapan Journal of Fundamental Mathematics and Applications (JFMA)
I Nyoman Widana
Prodi Matematika FMIPA Universitas Udayana
Agriculture, Biological Sciences & Forestry Humanities Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Environmental Science Mathematics Mechanical Engineering Physics Transportation

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PENENTUAN PREMI DAN CADANGAN MANFAAT ASURANSI JIWA KREDIT PADA BANK UMUM NI LUH ROSITA DAMAYANTHI; I NYOMAN WIDANA; KARTIKA SARI
E-Jurnal Matematika Vol 12 No 1 (2023)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2023.v12.i01.p400

Abstract

Credit life insurance provides protection and guarantees to policyholders as debtors within the coverage period. Each insurance participant is required to pay premiums on time, namely at the beginning before the credit is issued by the bank. Net premiums can be determined using annuity calculations using the equivalence principle. Premium payments on credit life insurance are made at once taking into account mortality based on age, gender, and interest rates of 15.5% and 10.26% with a loan term of 8 years. The results of the analysis of the single premium value for the interest rate of 15.5% and 10.26% at the age of 36, 44, and 52 years showed that the interest rate and age had an effect on the premium price. The obligation of the insurance company is to pay claims to insurance participants. Insurance companies are required to have a benefit reserve fund to anticipate excess claims. Benefit reserves are the amount of money collected by the insurance company during the coverage period in preparation for claim payments. The calculation of benefit reserves in this study uses the prospective method. In the large calculation of the benefit reserves for interest rates of 15.5% and 10.26% at the age of 36, 44, and 52 years, the value of the benefit reserves decreased from the first year to the last year.
ESTIMASI CADANGAN KLAIM PADA ASURANSI UMUM DENGAN METODE CHAIN LADDER SUNDANIS AGUNG PERTIWI; I NYOMAN WIDANA; KARTIKA SARI
E-Jurnal Matematika Vol 12 No 1 (2023)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2023.v12.i01.p402

Abstract

Based on the 2020 Insurance Statistic Data released by OJK, the ratio of gross claims to gross premiums has increased due to the growth of gross premiums followed by increasing claims paid. Thus, the insurance company is obliged to provides claim reserve that is important to be estimated appropriately, especially outstanding claim reserves. This is because outstanding claim reserves are needed to cover underpayment on future claims. One popular method to estimate outstanding claim reserves is the Chain Ladder method. This study aims to determine the results of the estimated outstanding claim reserves on general insurance using Mack’s CL method. CL method is a method to estimate claim reserves simply without satisfying certain distribution assumptions. This study uses incremental run-off triangle data taken from Weindofer's research article (2012) with an event period of 2005-2012 and a development period of 8 years. Based on the calculations in this study, an estimated outstanding claim reserve of USD 20,109.82 was obtained, meaning the funds that must be prepared amounted to USD 20,109.82 in 2013 by the general insurance company that owns the data studied. It also serves as a benchmark in the determination of claim reserves in the 2013 financial statements
PENGARUH PERUBAHAN SUKU BUNGA TERHADAP NILAI POLIS ASURANSI PENDIDIKAN I GUSTI AYU VIDYARA VRAJESHVARI; I NYOMAN WIDANA; NI KETUT TARI TASTRAWATI
E-Jurnal Matematika Vol 13 No 2 (2024)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2024.v13.i02.p451

Abstract

Education insurance is an insurance product that provides financial protection for the continuity of a child's education. It offers certainty in funding a child's education. This research utilizes secondary data from the Mortality Table Indonesia IV 2019 and illustration data from an educational insurance policy offered by an insurance company. The data analysis method involves the use of Python programming language, and the steps include determining the Mortality Table for joint life insurance, creating a model to calculate the annual premium and policy value based on the contract specified in the policy, developing software to calculate the premium and policy value using the generated model, and determining the premium and policy value using the software. The aim of this research is to determine the effect of changes in interest rate on the volicy value. Based on the case study and using the developed software, it is found that the premium price and policy value of education insurance will change when the interest rates change. The premium price will decrease, and the policy value will be smaller when the interest rates increase.
PERHITUNGAN PREMI ASURANSI MENGGUNAKAN SELECT DAN NON-SELECT TABLE PADA ASURANSI JOINT LIFE NI LUH PUTU SRI WAHYUNI; I NYOMAN WIDANA; KARTIKA SARI
E-Jurnal Matematika Vol 13 No 1 (2024)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2024.v13.i01.p434

Abstract

One of the basics in calculating insurance premiums is life table. There are two types of life tables, namely select and non select table. The purpose of the study was to calculate premiums using a select table with a two-year select period and a non-select table in term joint life insurance for 10-term insurance and endowment insurance. The select tables used are select life table with a two-year select period and non- select life table model. The result obtained is that the premium value in term joint life insurance for 10-term insurance and endowment insurance calculated using the select table model is smaller than using the non- select table. Beside that, it is obtained that the difference gets bigger as the couple gets older.
FROZEN INITIAL LIABILITY METHOD TO DETERMINE NORMAL COST OF PENSION FUND WITH VASICEK INTEREST RATE MODEL Sulma, Sulma; Rasyid, Nur Ahniyanti; Widana, I Nyoman
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 2 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i2.20150

Abstract

Civil servants have an important role in national development, so increasing their productivity is needed. The pension fund program is given as a form of effort by government agencies to ensure employee welfare when entering retirement. This research discusses the normal cost of the defined benefit pension program using one of the actuarial valuation methods, namely Frozen Initial Liability (FIL), by taking into account the stochastic interest rate following the Vasicek model. The data used in this study are lecturers majoring in MIPA, Faculty of Science and Technology, Universitas Jambi, consisting of 8 people of female gender with the status of being a participant since 2022. Based on the calculation results obtained that in the period 0-30 years, the normal cost for each group member is constant, namely  per year or  per month. When the working period entered 31 years, one by one the participants began to enter their retirement period, which resulted in a change in the normal cost value. At 38 years of service, there was only one participant with a normal cost of  per year or by  per month. Changes in normal cost tend to decrease when retirement program participants also decrease. In the period of more than 38 years, all participants have retired so that normal cost payments are stopped.
Penerapan Metode Zillmer dan Illinois Pada Perhitungan Cadangan Premi Asuransi Jiwa Joint Life Chandra, Veronica Celine; Widana, I Nyoman; Wijayakusuma, IGN Lanang
Jurnal Matematika Vol 13 No 1 (2023)
Publisher : Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2023.v13.i01.p159

Abstract

Joint life insurance is life insurance whose premium payments end at the first death of one of the insureds. This study aims to calculate the value of premium reserves using the Zillmer and Illinois methods for two insureds with data obtained from PT. Allianz where the insured is 33 and 29 years old with a protection period of 15 years, a premium payment period of 10 years. The Zillmer method uses prospective calculations as a basis for calculations that do not depend on the term of the product used, while the Illinois method is part of the prospective method by limiting costs charged to insurance participants with a limit of 20 years of payment. The results of this study are the value of premiums and premium reserves using the Zillmer and Illinois methods in this study are greater than the value of premiums and premium reserves from PT. Allianz. In the first year, the premium reserve value for the Zillmer method is IDR 80.005.964 while for the Illinois method is IDR 62.902.458 where the reserve value for the following year always increases with the reserve value for the Zillmer method being greater than the Illinois method. The premium reserves for the Zillmer and Illinois methods at the end of the year have the same value as the compensation value of IDR 1.130.000.000, which means that the insurance company is ready to provide compensation as much as promised to insurance participants.
Nilai Cadangan Premi Pada Asuransi Kesehatan Individu Dengan Menggunakan Metode New Jersey dan Fackler Damayanti, Ni Kadek Vivin; Widana, I Nyoman; Eka Dwipayana, I Made
Jurnal Matematika Vol 13 No 2 (2023)
Publisher : Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2023.v13.i02.p165

Abstract

Hospital individual healthcare insurance is a type of insurance that offers health benefits to insurance participants to cover the cost of hospitalization and medical treatment if they get sick. Premiums paid by insurance participants will be managed by the insurance company to fund the health costs of the insured. An insurance company's obligation to pay an amount of money that must be set aside by the insurance company at a later date is called a premium reserve. This research was conducted with the aim of finding out how much the premium reserves for individual health insurance are using the New Jersey and Fackler methods with a coverage period of 25 years assisted by the Indonesian Mortality Table IV. Using Fackler method the results of calculating premium of individual health insurance using Fackler method for participants aged 15th, 36th and 40th respectively and , with a compensation amount of . Besides this, the amount of reserves increased from the first year to the 19th year and decreased from the 20th year to the 25th year. In addition, it should be noted that the reserve value at the end of the t-year calculated using the New Jersey method is always smaller than the reserve value calculated using the Fackler method, for Keywords: Individual Health Insurance, Premium Reserve, New Jersey, Fackler
ANALISIS ASURANSI PENGANGGURAN DENGAN ASUMSI NON-ZERO MORTALITY Widana, I Nyoman; Winada Gautama, I Putu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 3 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (544.123 KB) | DOI: 10.30598/barekengvol15iss3pp575-580

Abstract

Indonesia dengan jumlah penduduk sekitar 267 juta jiwa memiliki angkatan kerja sangat besar. Tetapi jumlah lapangan kerja yang tersedia tidak mampu menyerap semua angkatan kerja ini. Selain itu angka pemutusan hubungan kerja juga relatif masih tinggi. Hal ini membuat pemerintah melontarkan wacana program asuransi pengangguran. Sejauh ini telah dilakukan studi tentang hubungan besar premi dan benefit dari asuransi pengangguran. Tetapi, model yang digunakan dalam perhitungan preminya, dibentuk berdasarkan asumsi zero mortality. Tujuan dari penelitian ini adalah menganalis asuransi pengangguran dengan asumsi non-zero mortality. Metode yang digunakan adalah The Equivalence Principle. Hasil Perhitungan menunjukkan tarif premi untuk non-zero mortality nilainya lebih kecil dari pada tarif premi untuk zero mortality.
COMPARISON OF PROJECTED UNIT CREDIT AND ENTRY AGE NORMAL METHODS IN PENSION FUND VASICEK AND COX-INGERSOLL-ROSS MODELS Sulma, Sulma; Widana, I Nyoman; Toaha, Syamsuddin; Fitria, Ita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2421-2432

Abstract

The pension program is one of the pension fund's efforts to anticipate the risks that will be experienced by participants in old age. Actuarial calculations help to determine the benefits that participants will receive by considering life chances, interest rates, age when becoming a participant, and normal retirement age. This study aims to determine normal contributions and actuarial liabilities with the Projected Unit Credit and Entry Age Normal methods using stochastic interest rates, namely Vasicek and Cox-Ingersoll-Ross (CIR). The data used in this study are civil servants who work at the Natural Resources Management Office, Bulukumba Regency. The results of the calculation analysis showed that normal cost using the Projected Unit Credit (PUC) method with the Vasicek and Cox-Ingersoll-Ross (CIR) model interest rates increased as the length of service increased, and at the end of the working period the Cox-Ingersoll-Ross (CIR) model interest rate reached Rp14.773.176,- which was higher than Vasicek by Rp3.849.898,-. The results of the calculation of normal cost using the Entry Age Normal (EAN) method with the Vasicek model increase in the period 0-20 years of service, then decrease towards the contribution value at the beginning of the service period of Rp1.499.725,-. At the beginning of the working year, the normal cost using the Entry Age Normal method with the Cox-Ingersoll-Ross (CIR) model interest rate is Rp7.581.593,- then decreases for 24 years of service to Rp5.849.854,- after which it increases again towards the initial contribution value of the working year. The results of the calculation of actuarial liabilities show an increase as the length of service increases, for the Entry Age Normal (EAN) and Projected Unit Credit (PUC) methods with the Cox-Ingersoll-Ross (CIR) interest rate model at the end of the service period, it is found that both are the same value, namely Rp443.195.285,-. By using the Vasicek interest rate model for both methods, the same result is obtained at the end of the service period of Rp115.496.951,-. This shows that the actuarial liabilities for both methods used are affected by interest rates, and the Cox-Ingersoll-Ross (CIR) model is higher than Vasicek
APPLICATION OF THE EQUIVALENCE PRINCIPLE TO THE CALCULATION OF EDUCATION INSURANCE PREMIUMS FOR VILLAGE-OWNED ENTERPRISES (BUMDes) Widana, I Nyoman; Suciptawati, Ni Luh Putu; Sulma, Sulma
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2555-2562

Abstract

Program Education plays a vital role in improving human resources. But on the other hand, education costs are not cheap. For this reason, people need to prepare education funds from an early age. One way is to take part in an education insurance program. This is a business opportunity that a village-owned enterprise (BUMDes) can run by offering education insurance services to the public. This research aims to develop and use programming software to calculate education insurance premiums offered by BUMDes. The method used is The Equivalence Principle method. Based on the case study, the premium price calculated using software that has been developed is very competitive – below market price, depending on the interest rate and fees charged.
Co-Authors AA Sudharmawan, AA AGUSTINA PAULA THERESIA PUTRI LAHALLO Ahmad Fitri Ahmad Fitri Anak Agung Gde Raka Dalem ANGGIE EZRA JULIANDA HUTAPEA AYU EKA FANNY DEVI Chandra, Veronica Celine Damayanti, Ni Kadek Vivin Desak Nyoman Trisnawati Desak Putu Eka Nilakusmawati DESI KURNIA SARI FARREL WILLIEARDAN FEMY AYU ASTITI Fitria, Ita GEDE SUMENDRA HANNY PANJAITAN I GEDE ARIS JANOVA PUTRA I GEDE BAGUS PASEK SUBADRA I GEDE DICKY ARYA BRAMANTA I GEDE ERY NISCAHYANA I GEDE PUTU MIKI SUKADANA I GUSTI AGUNG GEDE DWIPAYANA I GUSTI AYU KOMANG KUSUMA WARDHANI I Gusti Ayu Made Srinadi I GUSTI AYU MEIGAYONI LESTARI I GUSTI AYU VIDYARA VRAJESHVARI I Made Eka Dwipayana I MADE WAHYU WIGUNA I Nengah Artawan I Nengah Simpen I Putu Eka Nila Kencana I Putu Winada Gautama I WAYAN SANDY BAYU NUGRAHA I Wayan Sumarjaya Ida Ayu Eka Trisna Putri Ida Ayu Gede Widihati JENNE LALI TEWO JULIANTARI JULIANTARI K. Sari Kartika Sari Ketut Jayanegara Komang Dharmawan L. G. Astuti LIA JENITA LUH PUTU IDA HARINI MADE EDI HENDRAWAN MADE PUTRI ARIASIH NANDA NINGTYAS RAMADHANI UTAMI NI KETUT AYU MURNIASIH Ni Ketut Tari Tastrawati NI KOMANG AYU SEDANA DEWI NI KOMANG SUKANASIH NI LUH DE SISKA SARI DEWI NI LUH PUTU RATNA DEWI NI LUH PUTU RATNA DEWI NI LUH PUTU SRI WAHYUNI Ni Luh Putu Suciptawati NI LUH ROSITA DAMAYANTHI Ni Made Asih Ni Made Puspawati NI PUTU AYU DEWI CAHYANTARI NI PUTU MIRAH PERMATASARI NI WAYAN ASRI PRADNYANI Nur Ahniyanti Rasyid RAIN FERNANDO BANGUN RIZKA AULIA NOVALINDA SANI SAEFULOH SARAH VERONICA HUTABALIAN SISILIA MARTINA UTAMI AGUSTINI Sulma, Sulma SUNDANIS AGUNG PERTIWI syamsuddin Toaha Tjokorda Bagus Oka TRI YANA BHUANA ULFA DIANITA VALERIA TRISNA YUNITA VIKY AMELIAH Wijayakusuma, I Gusti Ngurah Lanang WIMAS ASTARI YUDA Winada Gautama, I Putu YOGI PRADIPTA YOHANES BAMBANG SUGIARTO